Convert DEGREES to RADIANS, Free
Type any DEGREES value and see the RADIANS result instantly. No button press needed.
How to convert DEGREES to RADIANS
Radians and degrees are two ways to measure angles. Degrees (out of 360) are what most people learn first and what you see on a protractor. Radians (out of 2 pi) are what nearly every programming language and mathematics library uses internally, because they make calculus and trigonometric identities come out cleanly. The conversion factor is pi / 180, so radians = degrees x (pi / 180).
The calculation is computed instantly in your browser using JavaScript's built-in Math.PI constant. Type your degree value and the radian equivalent appears right away, expressed as a decimal or a pi fraction depending on the format you select.
Enter the angle in degrees
Type the degree value. Common inputs are 30, 45, 60, 90, 180, and 360, but any decimal works.
Read the radian result
The converter displays the result in decimal radians. 90 degrees = 1.5708 radians (pi/2); 180 degrees = 3.14159 radians (pi).
Choose decimal or pi fraction format
If the tool supports it, select whether you want the output as a plain decimal or as a multiple of pi (for example 'pi/4' for 45 degrees).
Use the value in your code or formula
Paste the radian value into your trigonometric function call, shader code, or physics equation.
Frequently asked questions
What is the formula to convert degrees to radians?
Radians = degrees x (pi / 180). Or equivalently, multiply by 0.0174533 for a decimal approximation.
Why do programming languages use radians instead of degrees?
In calculus, the derivative of sin(x) is cos(x) only when x is in radians. This clean relationship simplifies a huge amount of mathematics in physics, graphics, and signal processing.
What is 45 degrees in radians?
45 x (pi/180) = pi/4 = approximately 0.7854 radians.
What is 360 degrees in radians?
360 x (pi/180) = 2*pi = approximately 6.2832 radians. One full rotation equals 2 pi radians.
How do I convert radians back to degrees?
Degrees = radians x (180 / pi). For example, pi/2 radians x 57.2958 = 90 degrees.